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함께 풀고 싶은 문제

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[창의 퍼즐] [대수] 쉬운 대수

infinitepi 2020.07.25 22:24 조회 625

문제 푼 사람 1명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

$x^{2}+y^{2}=18$

일 때,

$x^{4}+x^{2}y^{2}+y^4$ 의 최솟값과, 그때의 x,y의 값을 다 더하여라.

(풀이필수)

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세계최고수학자 Lv.1 2020.07.26 03:04

X y가 실수라 안 적혀있어서 실수라고 일단 하면 (x²+y²)²=324 이고 x⁴+y⁴+2x²y²=324 입니다 여기서 -x²y²을 더하면 x⁴+y⁴+x²y²이 나오구요 그럼 -x²y²의 최소값을 구하면 x⁴+y⁴+x²y²이 최솟값이 나옵니다 x²y²은 항상 0보다 크거나 같아요 전제조건을 실수라 잡았으니 0보다 크거나 같다는 당연하고 그러면 최솟값은 0이 되므로 x=0일때 y=+-18, x=+-18 일때 y=0 따라서 그 합은 +-18이네요

지나가던 중2 올림

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- infinitepi Lv.9 2020.07.26 03:13
  
  비댓 정답요청이요!!!!!!!!!!!!!!
  
  좋아요0
- infinitepi Lv.9 2020.07.26 03:14
  
  그리고 잘못써서 최솟값으로 바꿨어요
  
  좋아요0
SON7 Lv.5 2020.07.26 03:32

수의 범위가 복소수인가요, 실수인가요?

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- infinitepi Lv.9 2020.07.26 04:01
  
  실수요
  
  좋아요0
해결

도전

여백 패르마 Lv.5 2020.07.26 06:03 비밀댓글

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